Its relatively simple, They can't interact with any US Business, especially the financial institutions, even indirectly. So yes they can still transact in dollars so long as the transaction never touches the US Financial system in any way, but it would be risky for them to do so in my opinion.
Good luck with that. Unless the Guptas are trading in cash they are pretty much screwed. No bank with US currency or any US entity shareholding will knowingly transact with them.
Interestingly enough, USA doesn't seem to have mutual extradition treaty & legal assistance with UAE but South africa apparently signed it in 2018. Dubai seems safe haven for guptas for now unless NPA & UAE authorities pursue it with vigour.
Last I checked Dubai was a city of the United Arab Emirates. You don't do extradition treaties with cities. South Africa has to actually file the extradition papers for something to happen.
Of course, but the US Dollar is not the only currency, its just the most widely used for international transactions... it doesn't mean they can't do business, it just makes it complicated and more expensive.
It's extremely complicated as even international wire transfers have sponsor banks and entities to enable the movement of cash and technically any currency which comes into the possession of any US entity would result in it being seized.